Summary Statistics & Confidence Intervals

Annie HerbertMedical Statistician

Research & Development Support UnitSalford Royal NHS Foundation Trust

annie.herbert@manchester.ac.uk0161 2064567

Timetable

Time Task

60 mins Presentation

20 mins Coffee Break

90 minsPractical Tasks in

IT Room

Outline

• Sampling

• Summary statistics

• Confidence intervals

• Statistics Packages

‘Population’ and ‘Sample’

• Studying population of interest. Usually would like to know typical value and spread of outcome measure in population.

• Data from entire population usually impossible or inefficient/expensive so take a sample(even census data can have missing values).

• Sample must be representative of population.

• Randomise!

E.g. Randomised Controlled Trial (RCT)

POPULATION SAMPLE

RANDOMISATION

GROUP 1

GROUP 2

OUTCOME

OUTCOME

Types of Data

Categorical

Example:• Yes/No• Blood Group

Graphs:• Bar Chart• Pie Chart

Summary: • Frequency (n)• Proportion (%)

Numerical/Continuous

Example:• Weight• Pain Score

Graphs:• Histogram• Box and Whisker Plot

Summary:• Mean & Standard Deviation (SD)• Median & Inter-quartile range (IQR)

Types of Average(‘Average’ - a number which typifies a set of numbers)

• Mean = Total divided by n

• Median = Middle value

• Mode = Most common value/group(rarely used)

Types of Average - Example

Pain score data: 10, 8, 7, 7, 1, 7, 6, 5, 3, 4

Ordered: 1, 3, 4, 5, 6, 7, 7, 7, 8, 10

Mean = (1 + 3 + 4 + … + 10) ÷ 10 = 5.8Median = (6+7) ÷ 2 = 6.5Mode = 7

5th 6th 2nd 3rd 8th 9th

Median

Mean or Median?

0

5

10

15

20

-3 -1 1 3 5 7 9 11 13 15 17 19 21

0

10

20

30

40

50

0 1 2 3 4 5 6 7

Roughly Normally distributed: • Mean or median• Mean by convention

Skewed:• Median• Less affected by extreme values

Variation and Spread

• Standard Deviation (‘SD’)- Average distance from mean- Use alongside mean

• Inter-Quartile Range (‘IQR’)- Range in which middle 50% of the data lie(middle 50% when ordered)- Use alongside median

• Range- Highest and lowest value- Possibly quote in addition to SD/IQR

Types of Variation - Example

Pain score data: 10, 8, 7, 7, 1, 7, 6, 5, 3, 4

Ordered: 1, 3, 4, 5, 6, 7, 7, 7, 8, 10

SD = 2.6 IQR = (3.75, 7.25)Range = (1,10)

IQR

5th 6th 2nd 3rd 8th 9th

Median

Standard Error

• Not the same as standard deviation.

• Calculated using a measure of variability and sample size.

• Used to construct confidence intervals.

• Not very informative when given alongside statistics or as error bars on a plot.

Sample statistic is the best guess of the (true) population value

• E.g. Sample mean is the best estimate of mean in population.

• Mean likely to be different if take a new sample from the population.

• Know that estimate not likely to be exactly right.

Confidence Intervals (CIs)

• Confidence interval = “range of values that we can be confident will contain the true value of the population”.

• The “give or take a bit” for best estimate.

• Convention is to use a 95% confidence interval (‘95% CI’).

• But also leaves 5% confidence that this interval does not contain the true value.

Example: Legislation for smoke-free workplaces and health of bar workers in Ireland: before and

after study (Allwright et al; BMJ Oct 2005)

Before

N=138

After

N=138

Difference

(95% CI)

Salivary cotinine (nmol/l)

Median

29.0 5.1 -22.7 (-26.7 to -19.0)

Any respiratory symptoms

n (%)90 (65%) 67 (49%) -16.7 (-26.1 to -7.3)

Runny nose/sneezing

n (%)61 (44%) 48 (35%) -9.4 (-19.8 to 0.9)

Example: Supplementary feeding with either ready-to-use fortified spread or corn-soy blend in wasted adults

starting antiretroviral therapy in Malawi (MacDonald et al; BMJ May 2009)

“After 14 weeks, patients receiving fortified spread had a greater increase in BMI and fat-free body mass than those receiving corn-soy blend: 2.2 (SD 1.9) v 1.7 (SD 1.6) (difference 0.5, 95% confidence interval 0.2 to 0.8), and 2.9 (SD 3.2) v 2.2 (SD 3.0) kg (difference 0.7 kg, 0.2 to 1.2 kg), respectively.”

Example: Sample size mattersWhat proportion of patients attending clinic are satisfied?

Sample size

Number satisfied

Proportion satisfied

95% CI for proportion

10 7 70% 35% to 93%

25 18 70% 50% to 88%

50 35 70% 55% to 82%

100 70 70% 60% to 79%

1000 700 70% 67% to 73%

Example: % confidence matters

Sample size = 50

No. satisfied = 35

Proportion satisfied= 70%

90% CI 58% to 81%

95% CI 55% to 82%

99% CI 51% to 85%

What proportion of patients attending clinic are satisfied?

p-values vs. Confidence Intervals

• p-value:- Weight of evidence to reject null hypothesis- No clinical interpretation

• Confidence Interval:- Can be used to reject null hypothesis- Clinical interpretation- Effect size- Direction of effect- Precision of population estimate

So… it’s not all about p-values!

• For some hypotheses p-value and CI will both indicate whether to reject it or not.

• A CI will also provide an estimate, as well as a range for that estimate.

• General medical journals prefer CI.

Statistical PackagesPackage Summary Statistics Confidence Intervals

SPSS

• Not user-friendly• Gives a large choice of statistics to calculate

Doesn’t provide a CI for some key comparative statistics:

e.g. simple percentage

Stats

Direct

• One right-click• Will produce a set 20 or so of the most commonly used statistics

Provides a CI for most statistics

Thanks for listening!